What sample size is needed to give a margin of error within in estimating a population mean with 99% confidence, assuming a previous sample had .

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Complete Question

What sample size is needed to give a margin of error within ± 13 in estimating a population mean with 99% confidence, assuming a previous sample had s=116

The sample size n = 530 samples

Step-by-step explanation:

Margin of Error formula = z × standard deviation/√n

Margin of Error = ± 13

Standard deviation = 116

z = z score of 99% = 2.58

±13 = 2.58 × 116/√n

Cross Multiply

±13 × √n = 2.58× 116

±13 × √n = 299.28

√n = 299.28/±13

√n = ± 23.0215384615

Square both sides

(√n)² = (±23.0215384615)²

n = 529.991233134

Approximately , n = 530 samples

85 m.

Step-by-step explanation:

Use Pythagoras Theorem:

x^2 = 51^2 + 68^2

=  7225

x = √7225

= 85